Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated homeostatic systems experiencing multiple excitations. It focuses on the evolution of a signal (e.g., heart rate) before, during, and after excitations taking the system out of its equilibrium (e.g., physical effort during cardiac stress testing). Such approach can be applied to a broad range of outcomes such as physiological processes in medicine and psychosocial processes in social sciences, and it allows to extract simple characteristics of the signal studied. The model is based on a first order linear differential equation with constant coefficients defined by three main parameters corresponding to the initial equilibrium value, the dynamic characteristic time, and the reaction to the excitation. Assuming the presence of interindividual variability (random effects) on these three parameters, we propose a two-step procedure to estimate them. We then compare the results of this analysis to several other estimation procedures in a simulation study that clarifies under which conditions parameters are accurately estimated. Finally, applications of this model are illustrated using cardiology data recorded during effort tests.

Integrated Heart-Coupling multiscale and multiphysics models for the simulation of the cardiac function

Toni Mikael Lassila, Alfio Quarteroni, Simone Rossi, Ricardo Esteban Ruiz Baier

Mathematical modeling of the human heart and its function can expand our understanding of various cardiac diseases, which remain the most common cause of death in the developed world. Like other physiological systems, the heart can be understood as a complex multiscale system involving interacting phenomena at the molecular, cellular, tissue, and organ levels. This article addresses the numerical modeling of many aspects of heart function, including the interaction of the cardiac electrophysiology system with contractile muscle tissue, the sub-cellular activation contraction mechanisms, as well as the hemodynamics inside the heart chambers. Resolution of each of these sub-systems requires separate mathematical analysis and specially developed numerical algorithms, which we review in detail. By using specific sub-systems as examples, we also look at systemic stability, and explain for example how physiological concepts such as microscopic force generation in cardiac muscle cells, translate to coupled systems of differential equations, and how their stability properties influence the choice of numerical coupling algorithms. Several numerical examples illustrate three fundamental challenges of developing multiphysics and multiscale numerical models for simulating heart function, namely: (i) the correct upscaling from single-cell models to the entire cardiac muscle, (ii) the proper coupling of electrophysiology and tissue mechanics to simulate electromechanical feedback, and (iii) the stable simulation of ventricular hemodynamics during rapid valve opening and closure. (C) 2016 Elsevier B.V. All rights reserved.

Elsevier Science Sa2017

On the stability of blowup solutions for the critical corotational wave-map problem

Joachim Krieger, Shuang Miao

We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the scaling parameter

λ(t)=t−1−ν

is sufficiently close to

t−1

, i. e. the constant

ν

is sufficiently small and positive. The method of proof is inspired by [3,12], but takes advantage of geometric structures of the Wave Maps problem already used in [1,21] to simplify the analysis. In particular, we heavily exploit that the resonance at zero satisfies a natural first order differential equation.

2020

Towards Commoditizing Simulations of System Models Using Recurrent Neural Networks

Ahmet Caner Yüzügüler

System modeling and simulation plays a crucial role in the engineering of large and complex systems from various fields, such as industrial automation or power systems. In this paper, we propose a method that can be used to easily deploy high fidelity simulations at scale, onto various target platforms. Out method is to approximate the behavior of the modeled system using a recurrent neural network. We use artificial neural networks as they easily lend themselves to high performance execution, thus avoiding the need to (manually) translate system models (typically a system of differential equations) to specialized hardware architectures. Moreover, this approach is generic in the sense that it is decoupled from typical modeling and simulation tools, such as Matlab Simulink or Dymola. This paper presents a proof-of-concept neural network architecture including the methodology for training that we used to approximate the behavior of different example systems originating from the electrical power systems domain. We present our evaluation results mainly regarding accuracy and to a certain extent performance on a GPU-based testbed. Furthermore, we detail limitations of the used approach and outline potential directions for research regarding the general applicability of our method.

IEEE2018

On the stability of blowup solutions for the critical corotational wave-map problem

Joachim Krieger, Shuang Miao

λ(t)=t−1−ν

is sufficiently close to

t−1

, i. e. the constant

ν

2020